• Journal of Korean Association for Spatial Structures
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• v.24 no.1
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• pp.65-72
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• 2024

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.27-43
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• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.2
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• pp.198-208
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• 1995

Combining Iwan-Blevin's model into the approximated form of the nonlinear model derived for the dynamic analysis of the riser system with the inclusion of internal flow, current-vortex model is developed to investigate the effect of internal flow on vortex-induced vibration due to inline current The riser system includes a steadly flow inside the pipe which is modeled as an extensible or inextensible tubular beam. Galerkin's finite element approximation are implemented to derive the matrix equation of equilibrium for the finite element system. The investigations of the effect of internal flow on vibration due to inline current are performed according to the change of various parameters such as top tension, infernal flow velocity. current velocity, and so on. It is found that the effect of internal flow on vibration due to vortex shedding can be controlled by the increase of top tension. However, careful consideration has to be given, in design point in order to avoid the resonance band occurding near vortex shedding frequency, particularly for the long riser.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.1
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• pp.75-90
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• 1995

A mathematical model for the dynamic analysis of a riser system with the inclusion of internal flow and nonlinear effects due to large structural displacements is developed to investigate the effect of internal flow on marine riser dynamics. The riser system accounts fir the nonlinear boundary conditions and includes a steady flow inside the pipe which is modeled as an extensible or inextensible. tubular beam subject to nonlinear three dimensional hydrodynamic loads such as current or wave excitation. Galerkin's finite element approximation and time incremental operator are implemented to derive the matrix equation of equilibrium for the finite element system and the extensibility or inextensibility condition is used to reduce degree of freedom of the system and the required computational time in the case of a nonlinear model. The algorithm is implemented to develop computer programs used in several numerical applications. The investigations of the effect of infernal flow on riser vibration due to current or wave loading are performed according to the change of various parameters such as top tension, internal flow velocity, current velocity, wave period, and so on. It is found that the effect of internal flow can be controlled by the increase of top tension. However, careful consideration has to be given in the design point particularly for the long riser under the harmonic loading such as waves. And it is also found that the consideration of nonlinear effects due to large structural displacements increases the effect of internal flow on riser dynamics.